Reference Plane for Quadrilateral Element or Face

The plane vectors are calculated as:(1)

$${\mathit{PL}}_{\mathit{1}}\mathit{=}\mathit{\left(}{V}_{\mathit{3}}\mathit{+}{V}_{\mathit{2}}\mathit{\right)}\mathit{-}\mathit{\left(}{V}_{\mathit{1}}\mathit{+}{V}_{\mathit{4}}\mathit{\right)}$$

(2)

$${\mathit{PL}}_{\mathit{2}}=\mathit{\left(}{V}_{\mathit{3}}\mathit{+}{V}_{\mathit{4}}\mathit{\right)}\mathit{-}\mathit{\left(}{V}_{\mathit{1}}\mathit{+}{V}_{\mathit{2}}\mathit{\right)}$$

where, $V_1$ , $V_2$ , $V_3$ , and $V_4$ are the vectors that connect the four corner nodes with the centroid of the quadrilateral. These two plane vectors and the centroid are then used to construct the reference plane.

Figure 1. Vectors of a Non-warping Quadrilateral Face